Non-manipulability of uniform price auctions with a large number of objects

Abstract

When agents (bidders) have multi-demand preferences, uniform price auctions are generally not immune to agents' strategic manipulation, and they may achieve an inefficient allocation. We consider economies in which a large number of identical objects have to be allocated. Agents have quasi-linear preferences with non-increasing incremental valuations. We explore the incentives of agents in uniform price auctions. An important assumption on preferences is proposed, called "no monopoly." It requires that preferences should be correlated in such a way that no agent's incremental valuation for an additional object when he receives sufficiently many objects is higher than those of the other agents. We show that under no monopoly and other mild assumptions on preferences, as the number of objects goes to infinity, the payment in any uniform price auction converges to that in a Vickrey auction. We deduce that when there are sufficiently many objects, truth-telling is an approximate Bayesian Nash equilibrium in each uniform price auction.

No Price Envy in the Multi-unit Object Allocation Problem with Non-quasi-linear Preferences

“…One of the most important results in this strand of research is the inefficiency theorem: any equilibrium in the minimum uniform-price auction does not achieve an efficient allocation in general (Ausubel et al, 2014;Baisa, 2016). In a uniform-price auction, the truth-telling does not constitute an equilibrium, but it does an approximate equilibrium if there are many agents (Swinkers, 2001; Azevedo and Budish, 2019) or many objects (Tajika and Kazumura, 2019).…”